DeltaDoverD Progress

The goal

Fragmentation Function test

A complete test of independent fragmentation can be performed with polarized proton and neutron targets. The ratio of the difference of polarized to unpolarized cross sections for proton and neutron targets [math]\Delta R_{np}^{\pi^+ + \pi^-}[/math] can be written in terms of the structure functions:

[math]\Delta R_{np}^{\pi^+ + \pi^-} = \frac{\Delta \sigma_p^{\pi^+ + \pi^-} - \Delta \sigma_{n}^{\pi^+ + \pi^-}}{\sigma_p^{\pi^+ + \pi^-} - \sigma_{n}^{\pi^+ + \pi^-}}= \frac{g_1^p - g_1^n}{F_1^p - F_1^n}(x,Q^2)[/math]

Delta d over d

[math]\frac{\Delta d_v}{d_v}(x,Q^2) = \frac{\Delta \sigma_p^{\pi^+ \pm \pi^-} - 4\Delta \sigma_{2H}^{\pi^+ \pm \pi^-}}{\sigma_p^{\pi^+ \pm \pi^-} - 4\sigma_{2H}^{\pi^+ \pm \pi^-}} (x,Q^2)[/math]

1/24/2011

1.) Find energy range with substantial ND3, pi- events when B <0.

Ratio plot for Q^2 and X_{BJ}

once you find the Q^2 and X_BJ range holding a reasonable amount of data.

2.) Inclusive electron scattering ratio of

Inclusiveelectrons -vs- Q-squared	Inclusive Missing Mass (W) for 1.0 Q^2 <1.2
[[|300px|thumb|The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n) NH3 Target]]	[[|300px|thumb|The inclusive missing mass W for each torus setting. Dashed line is B>0 and solid line is B<0]]
[[|300px|thumb|The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n)]]ND3 Target	[[|300px|thumb|The inclusive missing mass W for each torus setting. Dashed line is B>0 and solid line is B<0]]
[[|300px|thumb|The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n)]] Both Targets	300px|thumb|The inclusive missing mass W for each torus setting. Dashed line is B>0 and solid line is B<0

3.) Semi Inclusive pion production ratios -vs- Q^2, Only electron cuts

/cache/mss/clas/eg1b/production/pass1/v4/4p2out/misc/dst/dst2828*

NH3 4.2-

28422 28423 28424 28425 28426 28427 28428 28429 28432 28433 28438 28439 28443 28445 28446 28447 28448 28449 28450 28456 28457 28458 28460 28461 28462 28463 28464 28467 28469 28471 28472 28473 28476 28478 28479

NH3 4.2+

28240 28242 28244 28245 28246 28247 28249 28250 28252 28253 28254 28255 28256 28260 28261 28262 28263 28264 28265 28266 28272 28274 28275 28276 28277

File locations http://www.jlab.org/Hall-B/secure/eg1/EG2000/nevzat/UPGRADE_DST/

/cache/mss/home/nguler/dst

Rates before and after requiring pions

all the cuts are applied, except NPHE>2.5 cut.

4.2 GeV, ND3 target, 98 files, B<0[math]\frac{\mbox{SemiInclusive Events}}{\mbox{Inclusive Events}}= 14.5% [/math]

4.2 GeV, ND3 target, 32 files, B>0[math]\frac{\mbox{SemiInclusive Events}}{\mbox{Inclusive Events}}= 4.4 %[/math]

The ratio for ND3 4.2 GeV data

Electron paddle selection

Inclusive

Electron Paddle Number(Inclusive, B<0, 4.2 GeV Beam, ND3 Target)	Electron Paddle Number(Inclusive, B>0, 4.2 GeV Beam, ND3 Target)

Semi-Inclusive

Electron Paddle Number(Semi-Inclusive, B<0, 4.2 GeV Beam, ND3 Target)	Electron Paddle Number(Semi-Inclusive, B>0, 4.2 GeV Beam, ND3 Target)

B>0, ND3 Electron paddle number=5

B<0, ND3 Electron paddle number=10

The Ratio

X_B	[math]\frac{ND3,Epaddle=5,B\gt 0}{ND3,Epaddle=10,B\lt 0}[/math] without pions	[math]\frac{ND3,Epaddle=5,B\gt 0}{ND3,Epaddle=10,B\lt 0}[/math] with pions
0.3	[math]1.01 \pm 0.02[/math]	[math] 1.2 \pm 0.1[/math]
0.35	[math]1.06 \pm 0.01[/math]	[math]1.1 \pm 0.06[/math]
0.4	[math]1.1 \pm 0.01[/math]	[math]1.03 \pm 0.08[/math]
0.45	[math]1.1 \pm 0.01[/math]	[math]1.1 \pm 0.09[/math]
0.5	[math]0.9 \pm 0.02[/math]	[math]0.6 \pm 0.2[/math]
0.55	[math]0.23 \pm 0.06[/math]	[math]0.13 \pm 0.5[/math]

The ratio for NH3 4.2 GeV data

Electron paddle selection

Inclusive

Electron Paddle Number(Inclusive, B<0, NH3 target, 4.2 GeV Beam)	Electron Paddle Number(Inclusive, B>0, NH3 target, 4.2 GeV Beam)

Semi-Inclusive

Electron Paddle Number(Semi-Inclusive, B<0, NH3 target, 4.2 GeV Beam)	Electron Paddle Number(Semi-Inclusive, B>0, NH3 target, 4.2 GeV Beam)

B>0, NH3 Electron paddle number=5

B<0, NH3 Electron paddle number=10

The Ratio

X_B	[math]\frac{NH3,Epaddle=5,B\gt 0}{NH3,Epaddle=10,B\lt 0}[/math] without pions	[math]\frac{NH3,Epaddle=5,B\gt 0}{NH3,Epaddle=10,B\lt 0}[/math] with pions
0.3	[math]1.02 \pm 0.01[/math]	[math] 1.2 \pm 0.03[/math]
0.35	[math]1.08 \pm 0.008[/math]	[math]1.01 \pm 0.02[/math]
0.4	[math]1.09 \pm 0.009[/math]	[math]1.04 \pm 0.02[/math]
0.45	[math]1.19 \pm 0.01[/math]	[math]1.1 \pm 0.03[/math]
0.5	[math]0.9 \pm 0.01[/math]	[math]0.8 \pm 0.03[/math]
0.55	[math]0.2 \pm 0.03[/math]	[math]0.18 \pm 0.09[/math]

1/31/11

Electron paddle number for B>0 is 5 and for B<0 - 10. The cut was applied on [math]X_B[/math] : [math]0.3\lt X_B\lt 0.6[/math]

Inclusive

1.) Overlap electron kinematic ([math]\theta[/math], W, Momentum) for B>0 and B<0 and ND3 and NH3.

(NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)

Electron Momentum((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))	Electron [math]\theta[/math] Angle((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)); can create angle cut on electron to be sure flipping B-field contains same electrons	W mass((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))

2.) Now plot ratio (B< 0/B>0) electron kinematic ([math]\theta[/math], W, Momentum) for ND3 and NH3. ( I expect 2 curves in one plot)

[math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]

Electron Momentum([math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])	Electron [math]\theta[/math] Angle([math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])	W mass([math]\frac{ND3 B\lt 0}{ND3 B\gt 0}[/math], [math]\frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])

2.) Target ratio (B< 0/B>0) Difference electron kinematic ([math]\theta[/math], W, Momentum) (Ration for ND3 target - Ratio for NH3 target). ( I expect 1 curves in one plot)

[math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math]

Electron Momentum ([math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])	[math]\theta[/math] Theta Angle([math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])	W mass([math]\frac{ND3 B\lt 0}{ND3 B\gt 0} - \frac{NH3 B\lt 0}{NH3 B\gt 0}[/math])

Semi-Inclusive

(NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0)

Electron Momentum((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))	Electron [math]\theta[/math] Angle((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))	W mass((NH3,B>0), (NH3,B<0), (ND3,B>0) && (ND3,B<0))

2

2/7/11

1.) Now look a specific electron kinematic which appear to have unity ratio. P=2.5 GeV, \theta =18 degrees

W	NH3,B<0	NH3,B>0	ND3,B<0	ND3,B>0	NH3,B>0 - NH3,B<0	NH3,B>0 - NH3,B<0
1.72	[math]1.2 X 10^{-5} \pm 0.05[/math]	[math]2.9 × 10^{-5} \pm 0.04[/math]	[math]11.8 x 10^{-5} \pm 0.05[/math]	[math]2.1125 × 10^{-5} \pm 0.075[/math]	1.7	-9.7
1.74	[math] 3.9× 10^{-5} \pm 0.03[/math]	[math] 9.0 × 10^{-5} \pm 0.02[/math]	3[math]8.5x 10^{-5} \pm 0.03[/math]	[math]7.25 × 10^{-5} \pm 0.05[/math]	5.1	-3.2
1.76	[math]5.0× 10^{-5} \pm 0.024[/math]	[math]10 x 10_{-5} \pm 0.02[/math]	[math]51.8x 10^{-5} \pm 0.025[/math]	[math]8.2 × 10^{-5} \pm 0.047[/math]	5.0	-43.6
1.78	[math]4.2 × 10^{-5} \pm 0.03[/math]	[math] 8.4 × 10^{-5} \pm 0.02[/math]	[math]40.4x 10^{-5} \pm 0.03[/math]	[math]7.3 × 10^{-5} \pm 0.05[/math]	4.2	-33.1
1.8	[math] 5.8 × 10^{-6} \pm 0.07[/math]	[math] 1.4 × 10^{-5} \pm 0.05[/math]	[math]6.2 × 10-5 \pm 0.07[/math]	[math]1.05 × 10^{-5} \pm 0.1[/math]	0.8	-5.2

2.) Semi-Inclusive using above electrons

Paddle Number	Pion Momentum

3.) Semi-Inclusive using above electrons and choosing a single paddle from 2.)

Pi+/Pi- hitting paddle #	Pi+/Pi- hitting paddle #

2/14/11

1.) Get all files

2.) Do semi-inclusive paddle number for pions again

3.) Paddle Number ratio (with more files in order to double check, the same cuts on electrons)

2/23/11

1.) Plot pi^-/pi^+ -vs paddle #

2.) Paddle 7 has ratio 0f 0.9. Plot W, Q^2 and M_{\pi}

W

Q^2

3.) Paddle 25 has ratio 0f 0.3. Plot W, Q^2, M (our goal is to determine if the detector has same efficiency for detector same reaction when the Torus filed is flipped)

W

Q^2

3/04/11

Table. 1 Pion Paddle Number ratio

• 1.) ND3Bn/NH3Bp

Pion Paddle Number	Number of Events ND3Bn	Number of Events NH3Bp	Ratio(ND3Bn/NH3Bp) [math]\pm[/math] error
3.89	81	69	0.4 [math]\pm[/math] 0.000896
4.89	84	87	0.33 [math]\pm[/math] 0.000595
5.89	84	76	0.38 [math]\pm[/math]0.000757
6.89	75	98	0.26 [math]\pm[/math]0.000488
7.89	91	123	0.25 [math]\pm[/math] 0.000348
8.89	115	141	0.28 [math]\pm[/math] 0.000283
9.89	207	254	0.28 [math]\pm[/math] 0.000117
10.89	212	300	0.24 [math]\pm[/math]0.000092
11.89	284	413	0.24 [math]\pm[/math]0.000057
12.89	322	501	0.22 [math]\pm[/math] 0.000043
13.89	359	521	0.24 [math]\pm[/math] 0.000040
14.89	365	565	0.22 [math]\pm[/math] 0.000036
15.89	415	523	0.27 [math]\pm[/math]0.000040
16.89	444	526	0.29 [math]\pm[/math] 0.000039
17.89	405	555	0.25 [math]\pm[/math] 0.000036
18.89	414	528	0.27 [math]\pm[/math] 0.000039
19.89	387	502	0.27 [math]\pm[/math] 0.000042
20.89	408	505	0.28 [math]\pm[/math] 0.000042
21.89	352	457	0.27 [math]\pm[/math] 0.000048
22.89	298	358	0.29 [math]\pm[/math] 0.000070
23.89	522	547	0.33 [math]\pm[/math] 0.000038
24.89	530	608	0.3 [math]\pm[/math] 0.000032
25.89	571	590	0.33 [math]\pm[/math] 0.000034
26.89	523	564	0.32 [math]\pm[/math] 0.000036
27.89	422	440	0.33 [math]\pm[/math] 0.000052
28.89	368	342	0.37 [math]\pm[/math] 0.000079
29.89	101	108	0.32 [math]\pm[/math] 0.000427

• 2.) ND3Bp/NH3Bn

Pion Paddle Number	Number of Events ND3Bp	Number of Events NH3Bn	Ratio(ND3Bp/NH3Bn) [math]\pm[/math] error
0.91	45	89	1.29 [math]\pm[/math]0.004556
1.91	86	127	1.73[math]\pm[/math] 0.002488
2.91	82	133	1.58[math]\pm[/math] 0.002361
3.91	91	330	0.71 [math]\pm[/math]0.000822
4.91	94	348	0.69 [math]\pm[/math]0.000766
5.91	125	360	0.89 [math]\pm[/math]0.000649
6.91	120	399	0.77 [math]\pm[/math]0.000594
7.91	148	443	0.86 [math]\pm[/math]0.000484
8.91	128	387	0.85 [math]\pm[/math]0.000595
9.91	121	510	0.61 [math]\pm[/math]0.000459
10.91	104	417	0.64 [math]\pm[/math]0.000607
11.91	145	449	0.83 [math]\pm[/math]0.000481
12.91	108	469	0.59 [math]\pm[/math]0.000528
13.91	113	449	0.64 [math]\pm[/math]0.000541
14.91	104	401	0.66 [math]\pm[/math]0.000631
15.91	98	427	0.59 [math]\pm[/math]0.000609
16.91	100	335	0.76 [math]\pm[/math]0.000774
17.91	70	316	0.57 [math]\pm[/math]0.000973
18.91	65	269	0.62 [math]\pm[/math]0.001189
19.91	56	270	0.53 [math]\pm[/math]0.001273
20.91	37	200	0.47 [math]\pm[/math]0.002111
21.91	27	149	0.46 [math]\pm[/math]0.003316
22.91	28	99	0.72[math]\pm[/math] 0.004942
23.91	32	112	0.73 [math]\pm[/math]0.004087
24.91	42	103	1.04[math]\pm[/math] 0.003963
25.91	25	70	0.91 [math]\pm[/math]0.007479
26.91	24	66	0.93 [math]\pm[/math]0.008105
27.91	27	39	1.77 [math]\pm[/math]0.014578
28.91	24	48	1.28 [math]\pm[/math]0.011546

W

Q^2

W

Q^2

3/21/11

1.) Efficiency Ratios.

• 0.a.) Table . [math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,ND_3,B\gt 0)}[/math]

Pion Paddle Number	[math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,ND_3,B\gt 0)}[/math]	error
1	0.52	0.00188670
2	0.56	0.00075818
3	0.55	0.00080325
4	1.31	0.00152123
5	1.44	0.00158249
6	1.18	0.00084919
7	1.26	0.00096229
8	1.19	0.00066468
9	1.12	0.00077990
10	1.5	0.00113494
11	1.45	0.00137556
12	1.22	0.00070398
13	1.65	0.00147872
14	1.47	0.00122783
15	1.63	0.00154233
16	1.57	0.00162007
17	1.38	0.00138704
18	1.68	0.00288459
19	1.68	0.00321234
20	1.65	0.00394896
21	2.23	0.00993885
22	2.42	0.01726570
23	1.29	0.00877380
24	1.17	0.00650948
25	0.74	0.00280451
26	1	0.00808644
27	1.25	0.01073753
28	0.84	0.00615573
29	1.11	0.00957284

• 0.b.) Table . [math]\frac{N(\pi^+,NH_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math]

Pion Paddle Number	[math]\frac{N(\pi^+,NH_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math]	error
1	0.61	0.00136217
2	0.58	0.00072875
3	0.56	0.00063600
4	1.16	0.00084147
5	1.09	0.00067329
6	1.22	0.00084552
7	1.26	0.00077718
8	1.3	0.00071299
9	1.35	0.00095814
10	1.91	0.00150046
11	1.6	0.00131397
12	1.32	0.00072210
13	1.71	0.00129895
14	1.46	0.00093334
15	1.93	0.00219770
16	1.76	0.00160711
17	1.29	0.00106561
18	1.63	0.00205808
19	1.49	0.00210549
20	1.87	0.00366838
21	2.01	0.00692445
22	1.73	0.00746426
23	1.51	0.00978854
24	1.5	0.00801872
25	1.01	0.00349049
26	0.86	0.00424348
27	1.04	0.00729985
28	0.69	0.00620402
29	1.12	0.01390308

Perhaps we see if the MAID model can tell us what this ratio should be

Media:NH3positivepionMAID.pdfMedia:ND3negativepionMAID.pdf

• 1.) Table 1. [math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math]

Pion Paddle Number	[math]N(\pi^+,ND_3,B\lt 0)[/math]	[math]N(\pi^-,NH_3,B\gt 0)[/math]	[math]\frac{N(\pi^+,ND_3,B\lt 0)}{N(\pi^-,NH_3,B\gt 0)}[/math]	error
1	77	65	0.4075770	0.0009842584
2	159	97	0.5639721	0.0006539302
3	149	105	0.4882354	0.0005272353
4	393	126	1.0731347	0.0007711509
5	444	141	1.0834182	0.0006573745
6	484	130	1.2809561	0.0008725428
7	496	140	1.2189500	0.0007440855
8	578	151	1.3169920	0.0007160697
9	471	127	1.2759964	0.0009002428
10	599	118	1.7465341	0.0013677534
11	497	115	1.4869309	0.0012131589
12	582	151	1.3261062	0.0007208959
13	588	121	1.6719536	0.0012616248
14	546	136	1.3812936	0.0008776225
15	558	92	2.0867894	0.0023701069
16	505	107	1.6238274	0.0014740763
17	454	115	1.3582830	0.0011103103
18	388	86	1.5522638	0.0019569046
19	359	80	1.5439624	0.0021696589
20	304	64	1.6342777	0.0032068058
21	272	44	2.1269069	0.0073027548
22	215	38	1.9466466	0.0083331144
23	119	29	1.4118261	0.0091055132
24	123	33	1.2823997	0.0068297700
25	102	45	0.7798659	0.0026920919
26	82	36	0.7836887	0.0037785779
27	99	28	1.2164924	0.0083029104
28	75	25	1.0321754	0.0084089279
29	88	19	1.5935340	0.0193377338
30	43	10	1.4794514	0.0470776577
31	30	5	2.0643508	0.1850680665
32	59	17	1.1940853	0.0172383351
33	83	24	1.1898689	0.0102416449
34	85	26	1.1248065	0.0086048876
35	93	24	1.3332266	0.0114363482
36	79	23	1.1817660	0.0108450951
37	34	9	1.2997764	0.0485842596
38	32	20	0.5504936	0.0068650227
39	38	4	3.2685555	0.4088076301
40	12	4	1.0321754	0.1313894981
41	30	10	1.0321754	0.0332392060
42	5	3	0.5734308	0.1216930868

• 2.) Table 2. [math]\frac{N(\pi^+,ND_3,B\gt 0)}{N(\pi^-,NH_3,B\lt 0)}[/math]

paddleNumber	[math]N(\pi^+,ND_3,B\gt 0)[/math]	[math]N(\pi^-,NH_3,B\lt 0)[/math]	[math]\frac{N(\pi^+,ND_3,B\gt 0)}{N(\pi^-,NH_3,B\lt 0)}[/math]	error
1	59	5	30.21	2.70258040
2	79	14	14.45	0.27652327
3	73	8	23.36	1.03300637
4	65	59	2.82	0.00822726
5	55	49	2.87	0.01094524
6	80	52	3.94	0.01185748
7	65	49	3.4	0.01183225
8	113	75	3.86	0.00675056
9	117	72	4.16	0.00756073
10	200	115	4.45	0.00393821
11	226	166	3.49	0.00192550
12	328	178	4.72	0.00213914
13	391	259	3.86	0.00105330
14	360	287	3.21	0.00081064
15	389	278	3.58	0.00090286
16	426	274	3.98	0.00098738
17	437	284	3.94	0.00092912
18	444	241	4.72	0.00135761
19	419	291	3.69	0.00085791
20	397	329	3.09	0.00064841
21	407	286	3.64	0.00087414
22	346	260	3.41	0.00096976
23	274	235	2.98	0.00105807
24	430	361	3.05	0.00056086
25	478	388	3.15	0.00051121
26	471	390	3.09	0.00050259
27	420	385	2.79	0.00049185
28	342	326	2.69	0.00062326
29	266	280	2.43	0.00076396
30	78	103	1.94	0.00337017
31	33	29	2.91	0.02416684
32	34	30	2.9	0.02293226
33	32	32	2.56	0.01999906
34	28	30	2.39	0.02171314
35	17	22	1.98	0.03411592
36	21	14	3.84	0.08345855
37	7	9	1.99	0.13036518
38	27	20	3.46	0.04582149
39	24	33	1.86	0.01863261
40	31	35	2.27	0.01710150
41	76	71	2.74	0.00617114
42	16	31	1.32	0.02201769
43	18	22	2.09	0.03411970
44	23	18	3.27	0.05209530

• 3.) Table 3. [math]\frac{N(\pi^-,ND_3,B\gt 0)}{N(\pi^+,NH_3,B\lt 0)}[/math]

Pion Paddle Number	[math] N(\pi^-,ND_3,B\gt 0)[/math]	[math]N(\pi^+,NH_3,B\lt 0)[/math]	[math]\frac{N(\pi^-,ND_3,B\gt 0)}{N(\pi^+,NH_3,B\lt 0)}[/math] [math]\pm[/math] error
0.91	45	89	1.29 [math]\pm[/math]0.004556
1.91	86	127	1.73[math]\pm[/math] 0.002488
2.91	82	133	1.58[math]\pm[/math] 0.002361
3.91	91	330	0.71 [math]\pm[/math]0.000822
4.91	94	348	0.69 [math]\pm[/math]0.000766
5.91	125	360	0.89 [math]\pm[/math]0.000649
6.91	120	399	0.77 [math]\pm[/math]0.000594
7.91	148	443	0.86 [math]\pm[/math]0.000484
8.91	128	387	0.85 [math]\pm[/math]0.000595
9.91	121	510	0.61 [math]\pm[/math]0.000459
10.91	104	417	0.64 [math]\pm[/math]0.000607
11.91	145	449	0.83 [math]\pm[/math]0.000481
12.91	108	469	0.59 [math]\pm[/math]0.000528
13.91	113	449	0.64 [math]\pm[/math]0.000541
14.91	104	401	0.66 [math]\pm[/math]0.000631
15.91	98	427	0.59 [math]\pm[/math]0.000609
16.91	100	335	0.76 [math]\pm[/math]0.000774
17.91	70	316	0.57 [math]\pm[/math]0.000973
18.91	65	269	0.62 [math]\pm[/math]0.001189
19.91	56	270	0.53 [math]\pm[/math]0.001273
20.91	37	200	0.47 [math]\pm[/math]0.002111
21.91	27	149	0.46 [math]\pm[/math]0.003316
22.91	28	99	0.72[math]\pm[/math] 0.004942
23.91	32	112	0.73 [math]\pm[/math]0.004087
24.91	42	103	1.04[math]\pm[/math] 0.003963
25.91	25	70	0.91 [math]\pm[/math]0.007479
26.91	24	66	0.93 [math]\pm[/math]0.008105
27.91	27	39	1.77 [math]\pm[/math]0.014578
28.91	24	48	1.28 [math]\pm[/math]0.011546

• 4.) Table 4. [math]\frac{N(\pi^-,ND_3,B\lt 0)}{N(\pi^+,NH_3,B\gt 0)}[/math]

Pion Paddle Number	[math]N(\pi^-,ND_3,B\lt 0)[/math]	[math]N(\pi^+,NH_3,B\gt 0)[/math]	[math]\frac{N(\pi^-,ND_3,B\lt 0)}{N(\pi^+,NH_3,B\gt 0)}[/math][math]\pm[/math] error
3.89	81	69	0.4 [math]\pm[/math] 0.000896
4.89	84	87	0.33 [math]\pm[/math] 0.000595
5.89	84	76	0.38 [math]\pm[/math]0.000757
6.89	75	98	0.26 [math]\pm[/math]0.000488
7.89	91	123	0.25 [math]\pm[/math] 0.000348
8.89	115	141	0.28 [math]\pm[/math] 0.000283
9.89	207	254	0.28 [math]\pm[/math] 0.000117
10.89	212	300	0.24 [math]\pm[/math]0.000092
11.89	284	413	0.24 [math]\pm[/math]0.000057
12.89	322	501	0.22 [math]\pm[/math] 0.000043
13.89	359	521	0.24 [math]\pm[/math] 0.000040
14.89	365	565	0.22 [math]\pm[/math] 0.000036
15.89	415	523	0.27 [math]\pm[/math]0.000040
16.89	444	526	0.29 [math]\pm[/math] 0.000039
17.89	405	555	0.25 [math]\pm[/math] 0.000036
18.89	414	528	0.27 [math]\pm[/math] 0.000039
19.89	387	502	0.27 [math]\pm[/math] 0.000042
20.89	408	505	0.28 [math]\pm[/math] 0.000042
21.89	352	457	0.27 [math]\pm[/math] 0.000048
22.89	298	358	0.29 [math]\pm[/math] 0.000070
23.89	522	547	0.33 [math]\pm[/math] 0.000038
24.89	530	608	0.3 [math]\pm[/math] 0.000032
25.89	571	590	0.33 [math]\pm[/math] 0.000034
26.89	523	564	0.32 [math]\pm[/math] 0.000036
27.89	422	440	0.33 [math]\pm[/math] 0.000052
28.89	368	342	0.37 [math]\pm[/math] 0.000079
29.89	101	108	0.32 [math]\pm[/math] 0.000427

Corrected one just has values of 1.

2.) Kinematic plots for all 8 conditions

4/4/11

1.) Document the electron efficiency -vs- paddle ( for each target separately) and pion efficiency -vs- paddle in thesis

Inclusive detected electrons -vs- Q-squared

The ratio of inclusive electrons detected in scintillator paddle #7 when Btorus >0 (B_p)to inclusive electrons detected by paddle 11 when B<0(B_n)

*Inclusive

Media:ND3andNH3electronpaddlenumberinclusive.pdf
Media:NH3Q2inclusive.pdfMedia:ND3Q2inclusive.pdf

• Semi Inclusive

Media:ND3electronpaddlenumbersemi_inclusive.pdfMedia:NH3electronpaddlenumbersemi_inclusive.pdf

2.) Compare to MAI2007 for paddles with unity pion efficiency ratios

Total Cross Section:

[math]\sigma = \sigma_{T} + \epsilon \sigma_{L} + \sqrt{2\epsilon(1 + \epsilon)}\sigma_{LT} cos{\phi_{\pi}}^{CM} + \epsilon \sigma{TT} cos2{\phi_{\pi}}^{CM} + h \sqrt{2\epsilon (1-\epsilon)}\sigma_{LT^{\prime}}sin{\phi_{\pi}}^{CM} [/math]

where

[math]{\phi_{\pi}}^{CM}[/math] is pion azimuthal angle in CM frame, [math]\epsilon[/math] - virtual photon polarization.

[math]\epsilon = (1 + 2(1 + \frac{\nu^2}{Q^2})tan^2\frac{\theta_e}{2})^{-1}[/math]

where [math]\nu=E_i - E_f[/math], (the difference between the initial and final energy of the electron).

[math]Q^2 = 4 E_i E_f sin^2\frac{\theta_e}{2}[/math] - Four momentum transferred square.

[math]\theta_e[/math] - electron scattering angle.

h - electron helicity.

[math]\left ( \begin{matrix} p_{\pi x}^{LAB{\prime}} \\ p_{\pi y}^{LAB{\prime}} \\p_{\pi z}^{LAB{\prime}} \end{matrix} \right )= \left [ \begin{matrix} cos {\theta}_x & 0 & -sin {\theta_x} \\ 0 & 1 &0 \\ sin {\theta_x} &0 & cos {\theta_x} \end{matrix} \right ] \left [ \begin{matrix} cos {\phi_{\gamma}} & sin {\phi_{\gamma}} & 0 \\ -sin {\phi_{\gamma}} & cos {\phi_{\gamma}} &0 \\ 0 &0 & 1 \end{matrix} \right ] \left ( \begin{matrix} p_{\pi x}^{LAB} \\p_{\pi y}^{LAB} \\ p_{\pi z}^{LAB} \end{matrix} \right ) = [/math]

[math]= \left ( \begin{matrix} cos {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{LAB} + sin {\phi_{\gamma}} p_{\pi y}^{LAB}) - sin {\theta}_x p_{\pi z}^{LAB} \\ -sin {\phi_{\gamma}} p_{\pi x}^{LAB} + cos {\phi_{\gamma}} p_{\pi y}^{LAB} \\ sin {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{LAB} + sin {\phi_{\gamma}} p_{\pi y}^{LAB}) + cos {\theta}_x p_{\pi z}^{LAB} \end{matrix} \right ) [/math]

[math]{\phi}_{\pi}^{LAB{\prime}} = tan^{-1}(\frac{{p_{\pi y}}^{LAB{\prime}}}{{p_{\pi x}}^{LAB{\prime}}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{LAB} + cos{\phi_{\gamma}} \times p_{\pi y}^{LAB}}{cos {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{LAB} + sin {\phi_{\gamma}} p_{\pi y}^{LAB}) - sin {\theta}_x p_{\pi z}^{LAB}})[/math]

[math]{\phi}_{\pi}^{CM} = tan^{-1}(\frac{{p_{\pi y}}^{CM}}{{p_{\pi x}}^{CM}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{CM} + cos{\phi_{\gamma}} \times p_{\pi y}^{CM}}{cos {\theta}_x (cos {\phi_{\gamma}} p_{\pi x}^{CM} + sin {\phi_{\gamma}} p_{\pi y}^{CM}) - sin {\theta}_x p_{\pi z}^{CM}})[/math]

[math]p_{\pi x}^{CM} = p_{\pi x}^{LAB}[/math]

[math]p_{\pi y}^{CM} = p_{\pi y}^{LAB}[/math]

[math]p_{\pi z}^{CM} = -E_{\pi} \gamma_{CM} \beta_{CM} + p_{\pi z}^{LAB} \gamma_{CM}[/math]

where

[math]\phi_{\gamma} = tan^{-1}(\frac{p_{e y}^{\prime}}{p_{e x}^{\prime}})[/math]

[math]\theta_x = cos^{-1}(\frac{p_{e z}^{\prime} - p_{e z}}{\sqrt{{p_{e x}^{\prime}}^2 + {p_{e y}^{\prime}}^2 + ({p_{e z}^{\prime} - p_{e z}})^2}})[/math]

[math]\beta_{cm} = \frac {p_e}{m_p + E_e}[/math]

[math]\gamma_{cm} = \frac{1}{\sqrt{1 - \beta_{cm}^2}}[/math]

Media:NH3positivepionMAID.pdfMedia:ND3negativepionMAID.pdf

4/11/11

1.) Document the electron efficiency -vs- paddle ( for each target separately) and pion efficiency -vs- paddle in thesis

Zoom in on the Q^2 range from 0.9 to 1.3 fine binning.

2.) Media:X_BEpaddlenumber5and10.pdf